Problem: The grades on a history midterm at Gardner Bullis are normally distributed with $\mu = 75$ and $\sigma = 3.0$. Daniel earned a $72$ on the exam. Find the z-score for Daniel's exam grade. Round to two decimal places.
A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Daniel's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{72 - {75}}{{3.0}}} $ ${ z \approx -1.00}$ The z-score is $-1.00$. In other words, Daniel's score was $1.00$ standard deviation below the mean.